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Why Use a Fuzzy Partition in F-Transform?

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Department of Computer Science, University of Texas at El Paso, El Paso, TX 79968, USA
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Department of Teacher Education, University of Texas at El Paso, El Paso, TX 79968, USA
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Faculty of Economics, Chiang Mai University, Chiang Mai 50200, Thailand
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Author to whom correspondence should be addressed.
Axioms 2019, 8(3), 94; https://doi.org/10.3390/axioms8030094
Received: 21 April 2019 / Revised: 31 July 2019 / Accepted: 1 August 2019 / Published: 2 August 2019
(This article belongs to the Special Issue Fuzzy Transforms and Their Applications)
In many application problems, F-transform algorithms are very efficient. In F-transform techniques, we replace the original signal or image with a finite number of weighted averages. The use of a weighted average can be naturally explained, e.g., by the fact that this is what we get anyway when we measure the signal. However, most successful applications of F-transform have an additional not-so-easy-to-explain feature: the fuzzy partition requirement that the sum of all the related weighting functions is a constant. In this paper, we show that this seemingly difficult-to-explain requirement can also be naturally explained in signal-measurement terms: namely, this requirement can be derived from the natural desire to have all the signal values at different moments of time estimated with the same accuracy. This explanation is the main contribution of this paper. View Full-Text
Keywords: F-transform; fuzzy partition; measurement; measurement accuracy F-transform; fuzzy partition; measurement; measurement accuracy
MDPI and ACS Style

Kreinovich, V.; Kosheleva, O.; Sriboonchitta, S. Why Use a Fuzzy Partition in F-Transform? Axioms 2019, 8, 94.

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